Sequent calculus
STYLE OF FORMAL LOGICAL ARGUMENTATION
Gentzen-style system; Gentzen system; Gentzen calculus; System LK; System LJ; Gentzen systems; Inference lines; Reduction tree; Reduction trees; Inference line
In mathematical logic, sequent calculus is a style of formal logical argumentation in which every line of a proof is a conditional tautology (called a sequent by Gerhard Gentzen) instead of an unconditional tautology. Each conditional tautology is inferred from other conditional tautologies on earlier lines in a formal argument according to rules and procedures of inference, giving a better approximation to the natural style of deduction used by mathematicians than to David Hilbert's earlier style of formal logic, in which every line was an unconditional tautology.